Why isn't Old Spock hanging out with nuSarek?

I don't read much of the surrounding non-screen materials of the Abramsverse, so I don't know what's supposed to have happened with nuSarek between Star Trek XI and STID. It seems like every other character who had a decent-sized role in the previous movie and didn't die came back in STID except Sarek.

So Spock Prime is off on the New Vulcan colony. Is Sarek there? And if not, why not? Spock Prime and Sarek Prime had a troubled relationship, but that seems to not be as much the case in the Abramsverse. Wouldn't Spock Prime appreciate the opportunity to get more time with Sarek? To look on it as a second chance at a better relationship?

There is a deleted scene in ST09 when nuSarek encounters Spock Prime. However they don't actually meet face to face, IIRC. We don't know if they ever did meet; although since Spock Prime was so adamant about not giving his younger self any details about his future (as we saw in STID), I doubt it. Spock Prime probably uses a pseudonym.

What gets me is in the last movie it is Spock prime who tells his younger self that he has located a planet suitable for Vulcans. How did Spock prime become that important in such little time to determine which planet for them to relocate to? If he did then surely Sarek is well aware of him by this time. The Enterprise crew sure is as seen in this movie. If not then new Spock should have got Uhura to patch the communication between him and Spock prime in his quarters or some private location near the bridge so nobody would know there were two of them.

How did Spock prime become that important in such little time to determine which planet for them to relocate to?

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I don't think it takes much time to go over Federation data on uninhabited Minshara class planets and Spock meddling with politics, well, this is what he has done the last years on Romulus so it is hardly surprising that he continues his activities instead of simply doing nothing.